Magnitude

Pre - Requisite / (Positive & Negative) Exponents
Standard / 8.EE.3 Use number expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is that the other.
8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
Student Outcomes /
  • Students know that positive powers of 10 are very large numbers, and negative powers of 10 are very small numbers.
  • Students know that the exponent of an expression provides information about the magnitude of a numbers.
  • Students compare and estimate quantities in the form of a single digit times a power of 10.
  • Students use their knowledge of ratios, fractions, and laws of exponents to simplify expressions.

Media /
Despicable Me - Vector
Procedure
HW / #16
Spiral Review #4
WKSP

Compare the following:

105 1050105 10-510-5 10-50

Powers of 10

Let M represent the world population as of March 23, 2013. (M ≈ 7,073,981,143)

How many digits does this number have?

Compare: M 1010

We say that the 10th power of 10 exceedsM.

Let M represent the US national debt on March 23, 2013. (M ≈ 16,755,133,009,522 to the nearest dollar)

What is the smallest power of 10 that can exceed M?

Exercise: Find the smallest power of 10 that will exceed M.

1. / Let M = 993,456,789,098,765
2. / Let M =

What kind of exponent represents a very small number?

The average ant weighs 0.0003 grams.

0.0003 = =

01

The mass of a neutron is 0.000 000 000 000 000 000 000 000 001 674 9 kilograms.

We would need to swing the decimal 27 place values before a digit appears!

What power of 10 can be used to simplify the mass of a neutron?

Exercise: Express each small number as a negative power of 10.

1. / The chance of having the same DNA as another person is approximately 1 in 10 trillion.

3. / The chance of winning a big lottery prize is about 10-8, and the chance of being struck by lightning in the US in any given year is about 0.000001. Which do you have a greater chance of experiencing? Explain.

Estimating Quantities

Example: In 1723, the population of NY City was about 7,248. By 1870, almost 150 years later, the population had grown to 942,292. Approximately, how many times greater was the population in 1870 compared to 1723?

‘Approximately’ signals us to use powers of 10. Thank goodness!

Population in 1723

Population in 1870

‘Times’ signals that multiplication was exercised to get to the population in 1870. We’re reversing the process. What operation should we use?

Running theme in math ( will help us finish the problem.

Exercise:

1. / The Federal Reserve states that the average household in January of 2013 had $7,122 in credit card debt. About how many times greater is the US national debt, which is $16,755,133,009,522?
2. / About how many times greater is the population of NY State (19,570,261) compared to that of NY City (8,336,697)?

Precision

If we want to get more precise, we can go down a place value.

NY State: 19,570,261 rounded to the nearest million is ______= 2 x 10?

NY City: 8,336,697 rounded to the nearest million is ______= 8 x 10?

We now have: ______

Exercise:

1. / There are about 9 billion devices connected to the internet. If a wireless router can support 300 devices, how many wireless routers are necessary to connect all 9 billion devices wirelessly?
2. / The average American household spends about $40,000 each year. If there are about 1 x 108 households, what is the total amount of money spent by American households in one year?

Name: ______Date: ______

Pre-AlgebraExit Ticket

1. / Let M = 118,526.65902. Find the smallest power of 10 that will exceed M.
2. / The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of 10.
If the average American lives about 80 years (or about 30,000 days), how many total breaths will a person take in her lifetime?

Name: ______Date: _____

Pre-AlgebraHW #16

1. Place each of the following numbers on a number line in its approximate location.

10-9910-17101410-51030

Express the following using positive exponents. Then represent as a rational number.

2. / What is the smallest power of 10 that would exceed 987,654,321,098,765,432?
3. / Which number is equivalent to 0.0000001? 107 or 10-7? How do you know?
4. / Sarah said that 0.00001 is bigger than 0.001 because the first number has more digits to the right of the decimal point. Is Sarah correct? Explain your thinking using negative powers of 10 and the number line.
5. / There are about 100 million smartphones in the US. Your friend has a smartphone. What share of US smartphones does your friend have?

6. / There are about 3,000,000 students attending school, kindergarten through 12th grade, in New York. Express the number of students as a single-digit integer times a power of 10.
The average number of students attending a middle school in New York is 8 x 102. How many times greater is the overall number of k-12 students compared to the number of middle school students?

Review:

7. / Divide the following:
a. 94.24 4 =b. 24.68 0.2 =
c.
8. / Simplify the following:
a. b.
c. d.